1. the probability of a basketball player hitting a foul shot is 1/3. how many shots would you expect her to make in 90 attempts.
a. 30
b. 60
c. 3
d. 45
my answer is b?
2. simplify 8P3.
a. 42
b. 336
c. 40,432
d. 56
my answer is d?
3. how many ways can 4 students be chosen from a class of 12 to represent their class at a banquet?
a. 495
b. 990
c. 5,940
d. 11,880
my answer is a?
4. you and 4 friends go to a concert. in how many ways can you sit in the assigned seats?
a. 20
b. 24
c. 48
d. 120
my answer is b?
5. you own 6 pairs of jeans and want to take 2 of them with you on vacation. in how many ways can you choose 2 pairs of jeans?
a. 10
b. 12
c. 15
d. 20
my answer is c?
1. Well, if the probability is 1/3, then we can expect her to make one shot out of every three attempts. So, in 90 attempts, we can expect her to make around 30 shots. So, the answer is indeed a. 30.
2. Ah, the classic problem of simplifying permutations. Well, 8P3 means we have 8 items and we're choosing 3 of them. So, the formula for permutations is n! / (n-r)! which gives us 8! / (8-3)! = 8! / 5! = 8 * 7 * 6 = 336. So, the answer is b. 336.
3. Now, for this question, we are choosing 4 students out of 12. This is a combination problem, so we use the combination formula nCr = n! / (r!(n-r)!). Plugging in the numbers, we get 12! / (4!(12-4)!) = 12! / (4!8!) = (12*11*10*9) / (4*3*2*1) = 495. So, the answer is indeed a. 495.
4. Ah, the good old seating arrangement problem! Well, with you and 4 friends, we have a total of 5 people. Each of you can sit in one of the 5 assigned seats, giving us 5 choices for the first person, 4 choices for the second person, 3 choices for the third person, 2 choices for the fourth person, and 1 choice for the last person. So, the total number of ways is 5 * 4 * 3 * 2 * 1 = 120. So, the answer is indeed d. 120.
5. Oh, the joy of choosing jeans! Well, you have 6 pairs of jeans and you want to choose 2 pairs. This is a combination problem, so we once again use the combination formula. 6C2 = 6! / (2!(6-2)!) = 6! / (2!4!) = (6 * 5) / (2 * 1) = 15. So, the answer is indeed c. 15.
Well, my friend, I hope my clownish explanations have entertained you along with providing the correct answers!
1. To find the expected number of shots made, we can multiply the probability of making a shot by the number of attempts. Given that the probability of making a shot is 1/3 and there are 90 attempts, the expected number of shots made would be (1/3) * 90 = 30. Therefore, the correct answer is option a) 30.
2. The formula for permutations is given by nPr = n! / (n - r)! Here, we have 8 objects and we need to arrange them in groups of 3. Therefore, we can calculate 8P3 as 8! / (8 - 3)! = 8! / 5! = 8 * 7 * 6 = 336. Hence, the correct answer is option b) 336.
3. The number of ways to choose r objects from a set of n objects is given by the combination formula nCr = n! / (r! * (n - r)!). In this case, we want to choose 4 students from a class of 12 to represent their class at the banquet. So, we can calculate 12C4 = 12! / (4! * (12 - 4)!) = 12! / (4! * 8!) = (12 * 11 * 10 * 9) / (4 * 3 * 2 * 1) = 495. Therefore, the correct answer is option a) 495.
4. If you and your 4 friends go to a concert and want to find the number of ways you can sit in the assigned seats, you need to calculate the number of permutations of 5 objects. Therefore, 5P5 = 5! = 5 * 4 * 3 * 2 * 1 = 120. Hence, the correct answer is option d) 120.
5. To determine the number of ways you can choose 2 pairs of jeans out of 6 pairs, you need to calculate the number of combinations. Therefore, 6C2 = 6! / (2! * (6 - 2)!) = 6! / (2! * 4!) = (6 * 5) / (2 * 1) = 15. So, the correct answer is option c) 15.
1. To determine the number of foul shots the basketball player is expected to make in 90 attempts, we can multiply the probability of making a shot (1/3) by the number of attempts (90). The expected number of shots made is (1/3) * 90 = 30. So, the correct answer is a. 30.
2. To simplify 8P3 (also known as the permutation of 8 items taken 3 at a time), we use the formula for permutation: nPr = n! / (n - r)!. In this case, it is 8! / (8 - 3)! = 8! / 5! = 8 * 7 * 6 = 336. So, the correct answer is b. 336.
3. To determine the number of ways to choose 4 students from a class of 12, we can use the combination formula: nCr = n! / (r!(n - r)!). In this case, it is 12! / (4!(12 - 4)!) = 12! / (4! * 8!) = (12 * 11 * 10 * 9) / (4 * 3 * 2 * 1) = 495. So, the correct answer is a. 495.
4. When you and your 4 friends go to a concert and want to sit in assigned seats, the number of ways to arrange yourselves is equal to the number of permutations of 5 items (you and your 4 friends) taken 5 at a time. So, it is 5P5 = 5! = 5 * 4 * 3 * 2 * 1 = 120. Therefore, the correct answer is d. 120.
5. To determine the number of ways to choose 2 pairs of jeans from 6 pairs, we can use the combination formula: nCr = n! / (r!(n - r)!). In this case, it is 6! / (2!(6 - 2)!) = 6! / (2! * 4!) = (6 * 5) / (2 * 1) = 15. So, the correct answer is c. 15.
on question 1 i meant to say
the probability of a basketball player hitting a foul shot is 1/3.
1) It is 1/3 of 90
2) 8! divided by 5!
3) is a combination
12! divide by (4!8!)
4) I agree with you
5) I agree with you.